To find the weight in lb. per lineal foot of square bars of metal.
Set index of B to weight of 12 cubic inches of the metal (_i.e._, one
lineal foot, 1 square inch in section) on A, and over the side of the
square in inches on C read weight in lb. on A.
EX.—Find the weight per foot length of 4½in. square wrought-iron bars.
Set middle index of B to 3·33 on A, and over 4½ on C read 67·5 lb. on
A.
(N.B.—For other metals use the corresponding constant in column (2),
below).
To find the weight in lb. per lineal foot of round bars.
Set R.H. or L.H. index of B to weight of 12 cylindrical inches of the
metal on A (column (4), below), and opposite the diameter of the bar in
inches on C, read weight in lb. per lineal foot on A.
EX.—Find the weight of 1 lineal foot of 2 in. round cast steel.
Set L.H. index of B to 2·68 on A, and over 2 on C read 10·7 lb. on A.
To find the weight of flat bars in lb. per lineal foot.
Set the breadth in inches on C to (1)/(weight of 12 cub. in.) of the
metal (column (3), below) on D, and above the thickness on D read weight
in lb. per lineal foot on C.
EX.—Find the weight per lineal foot of bar steel, 4½in. wide and ⅝in.
thick.
Set 4·5 on C to 0·294 on D, and over 0·625 on D read 9·56 lb. per
lineal foot on C.
To find the weight per square foot of sheet metal, set the weight per
cubic foot of the metal (col. 1) on C to 12 on D, and
────────────┬──────────┬──────────┬──────────┬───────────
│ (1) │(2) │ (3) │ (4)
│Weight in │Weight of │ (1)/(Wt. │ Weight of
Metals. │ lb. per │12 cubic │of 12 cub.│ 12
│cubic ft. │in. │ in.) │cylindrical
│ │ │ │ in.
────────────┼──────────┼──────────┼──────────┼───────────
Wrought iron│480 │3·33 │0·300 │2·62
Cast iron │450 │3·125 │0·320 │2·45
Cast steel │490 │3·40 │0·294 │2·68
Copper │550 │3·82 │0·262 │3·00
Aluminium │168 │1·166 │0·085 │0·915
Brass │520 │3·61 │0·277 │2·83
Lead │710 │4·93 │0·203 │3·87
Tin │462 │3·21 │0·312 │2·52
Zinc (cast) │430 │2·98 │0·335 │2·34
„ (sheet) │450 │3·125 │0·320 │2·45
────────────┴──────────┴──────────┴──────────┴───────────
above the thickness of the plate in inches on D read weight in lb. per
square foot on C.
EX.—Find the weight in lb. per square foot of aluminium sheet ⅜in.
thick.
Set 168 on C to 12 on D, and over 0·375 on D read 5·25 lb. on C.
To find the weight of pipes in lb. per lineal foot.
Set mean diameter of the pipe in inches (_i.e._, internal diameter
_plus_ the thickness, or external diameter _minus_ the thickness) on C
to the constant given below on D, and over the thickness on D read
weight in lb. per lineal foot on C.
┌────────────┬─────────────────────┬─────────────────────┐
│ Metals. │ Constant for Pipes. │Constant for Spheres.│
├────────────┼─────────────────────┼─────────────────────┤
│Wrought iron│ 0·0955 │ 6·87 │
│Cast iron │ 0·1020 │ 7·35 │
│Steel │ 0·0936 │ 6·73 │
│Brass │ 0·0882 │ 6·35 │
│Copper │ 0·0834 │ 6·00 │
│Lead │ 0·0646 │ 4·65 │
└────────────┴─────────────────────┴─────────────────────┘
EX.—Find the weight per foot of cast-iron piping 4 in. internal
diameter and ½in. thick.
Set 4·5 on C to 0·102 on D, and over 0·5 on D read 22·1 lb. on C, the
required weight.
To find the weight in lb. of spheres or balls, given the diameter in
inches. (W = 0·5236_d_^3 × wt. of 1 cub. in. of material).
Set the constant for spheres (given above) on B to diameter in inches on
A, and over diameter on C read weight in lb. on A.
EX.—Find the weight of a cast-iron ball 7½in. in diameter.
Set 7·35 on B to 7·5 on A, and over 7·5 on C read 57·7 lb. on A.
To find diameter in inches of a sphere of given weight.
Set the cursor to the given weight in lb. on A, and move the slide until
the same number is found on C under the cursor that is simultaneously
found on A over the constant for the sphere on B.
EX.—Find diameter in inches of a sphere of cast-iron to weigh 7½lb.
Setting the cursor to 7·5 on A, and moving the slide, it is found that
when 3·8 on C falls under the cursor, 3·8 on A is simultaneously found
over 7·35 on B. The required diameter is therefore 3·8 in.
The rules for cubes and cube roots (page 40) should be kept in view in
solving the last two examples.